scp upload is performed too late

Excerpt from build log:

Recording fingerprints
Sending e-mails to: <me>
[SCP] Connecting to <hostname>
ERROR: Failed to upload files
((many lines cut away))
Finished: UNSTABLE

(Same log as in JENKINS-7418)
The build is STABLE when Hudson sends e-mail, so I'm not told about the problem. However, the build is correctly marked UNSTABLE in the build list.
The next time the build runs and fails in the same way, I get an email stating that this job "is back to STABLE" which it very clearly isn't.
I suggest that uploading be done before Hudson sends out emails with status of the build.